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    Re: Statistical analysis of sight data to improve personal technique
    From: Jim Rives
    Date: 2022 May 9, 09:06 -0700

    Hi, Ed, 

    You last asked.. "So, I guess my question remains - what simple things analysis of sight data can one do to improve their 'seeing' and 'measurement'?"  

    Most people still practicing celestial probably are interested in "how they did", against some standard.  I have been exploring lunars in the past couple of years and have recently started analyzing my results over time.  Normally I take 5 moon-sun(or other objects)  observations per session and if time/inclination permits, take 6 sun-on-sun obserations to determine IE, three turning the micrometer drum clockwise, three counter clockwise.  (probably overkill but thought I'd see if there was any discernable difference on this sextant.)

    Each observation in a lunar observation session is entered into a little excel worksheet.  I decimalize, then caluclate the average LD and the GMT of the five shots. I apply the IC and have one version of the observed LD.  I then graph the 5 points and run a little straight line regression on the group using an excel regression routine.  That helps me see visually what the series looks like.  Then, taking a convenient time for x, apply that to the regression formula shown by excel in the graph, and find my second version of observed LD.  I then run each of these through ClockworkMappings (Frank's) Lunars Analyzer to find my error in lunar and the error in longitude and miles at my latitude.  The two results are quite different.    For example, my session yesterday yielded an Error in Lunar of 2.3' (or 67.8' of longitude) using excel's regression formula, but only -.23' (or 6.8' of longitude) when using my own calculation of mean values in the set.  The observation session before that yielded an Error of Lunar of 1.1' (34.0' of longitude) using the regression formula, but only .25' ( or 7.4' of longitude) using my own mean values. 

    So... my main question here is why the difference?  I would have expected the means and the regression approach to yield essentially the same answer.  Perhaps a regression on only 5 points is not useful?  So, in the interest in the pursuit of truth, I have decided to use my own calculations of means as the basis of determining longitude by lunars going forward.  Not only do I throw out observations that don't suit me, but whole methods of calculation!  But, seriously, if anyone with a statistics background can shed some light on why the two results are so different, please let me know. 

    And... back to IE.  I have been doing that pretty religiously and ultimately started recording that over time.  It never varies more than .1'.  Exept when one of my lunars was very far off.   I looked at the IE determination for the day and that was off too.  Next time I went out I checked my telescope on the sextant and it was somewhat out of focus, and once I carefully re-focused it, my IE was back to normal.  And the LD's were back in the range.  So, as to why record all of this, I have found that it helps one find errors they might not otherwise notice if they didn't have a trend to compare to.  

    I think the question of accuracy can only be thought of in terms of "accurate enough for what purpose".  Accuracy for surveying is a fine art, but is time consuming and expensive to do. (at least in the pre-aviation/space days).  Celestial at sea was pretty good at finding positions within a few miles... a big improvement over latitude sailing, and good enough.  Aviation required timliness over accuracy.  And now, GPS. It is really fascinating to see how society has invented means to reduce risk and cost by employing math/statistics.  

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